Holmstrom Retract argument

In any category, if $f = p \circ i$ and $f$ has the LLP wrt $p$, then $f$ is a retract of $i$. Dually, if $f$ has the RLP wrt $i$, then $f$ is a retract of $p$.

This implies that a map is a cofib (trivial cofib) iff it has the LLP wrt all trivial fibs (fibs), and the dual statement.

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